[Math 2.0] QUESTIONS PLEASE: Inviting Keith Devin to speak about his project

[Maria Droujkova]

Hello,

Several Math 2.0 members want to invite Keith to our weekly series and talk to him live about a math program his think tank envisions. I think we could have a valuable conversation, especially about OERs, grassroots movements, and blended financing. I would like everybody who reads this to ask a question they would ask Keith, as an experimental pre-meeting activity. One value this network has is in constructive, on-topic, deep questions we ask.

So, QUESTIONS PLEASE. I will start:

- Keith, do you want the resulting system to become an OER (open education resource) available worldwide? Why or why not?

~*~*~*~*~*
WANTED: An Apollo Program for Math

• No Related Post

Keith Devlin, Stanford University

The US ranks much worse than most of our economic competitors in the mathematics performance of high school students.

We now have the knowledge to turn that around. We could raise the level of mathematics performance across the board, within a single school generation, so that we are number one in the world. All it would take is a one-time, national investment of $100 million over a five-year period. That’s what it would cost to build and put in place a system that could achieve that change, with the existing school system and the existing teachers. Once built, that system would be self-sustaining.

That sounds like a lot of money for an upfront investment. But thought of as a national initiative, it’s peanuts. The payoff for the nation’s health and future prosperity is far greater than the long term benefits we got from the far greater investment in NASA’s Apollo Program to put a man on the Moon.

I don’t think it’s going to happen in this way, but not because people don’t think it’s a good idea. Rather, it would probably require a combination of nonprofit and for-profit funding that our system does not allow.

The same goal can, and surely will, be attained. But it will take a lot longer.
I’ll tell you, briefly, what the approach is, how I am so sure it will work, and where I got that cost figure. Everything I say is based on work that has already been done.

First, let me tell you who I am.

I’m a mathematician at Stanford who directs a multidisciplinary think tank called the H-STAR institute, that looks at issues involving human sciences and new technologies, with a view to improving technology design and use, including applications of technology in education at all levels. (I’m also the Math Guy on National Public Radio.)

What I want to tell you about is connected with the H-STAR institute, but is based on some work I’ve just completed as an individual, working with a large software company in Silicon Valley.

We have spent the past four years looking to see if we can use the range of today’s technologies to improve the dismal math performance level of the nation’s high school students.

The slide in math performance among US children occurs during the age range 8 to 13. Essentially the middle-school years. That was the target group for our study.

Many attempts have been made to improve US middle-school mathematics education, but all have failed to achieve the desired results. I think the reason is clear. They have all focused on improving basic math skills.

In contrast, I (and a great many of my colleagues) believe the emphasis should be elsewhere. Mathematics is a way of thinking about problems and issues in the world. Get the thinking right and the skills come largely for free.

There are two reasons why the focus has been on skills. First, many people, even those in positions of power and influence don’t understand what mathematics is and how it works. All they see are the skills, and they think, wrongly, that is what mathematics is about. (Given that for most people, their last close encounter with mathematics was a skills-based school math class, it is not hard to see how this misconception arises.)

The other reason is more substantial. For over two thousand years, the only way to provide mathematics education to the masses was through the written word. Textbooks. But in order to learn mathematical thinking from a textbook, you have to approach it via the skills. That means you have to master the skills first.

But as I already remarked, mathematics is not about acquiring basic skills or learning formulas. It’s a way of thinking. It’s not about things you know, it’s something you do. And the printed word is a terribly inefficient way to learn how to do something.

The best way for an individual to learn how to do something is, as the Nike slogan says, “Just do it!”

Until now, learning by doing was not a viable approach to mathematics education. It was possible one-on-one, by an apprenticeship system, but not on a broad scale. Now it can be done.

We now have the know-how to raise the mathematical performance of our nation’s schoolchildren in the 8 to 13 age-range to the top of the world rankings in a single school generation.

The method is simulation. That’s the way we train pilots to fly aircraft, the way we train astronauts to fly the shuttle and to work in the Space Station, the way we train surgeons, and the way the US Army trains soldiers before they go anywhere near the battlefield.

And that’s the way we should train young people to think mathematically.

The technology to do that has been provided to us by the leisure and entertainment industries. Basically, it’s videogame technology and Web 2.0 infrastructure.

No one has yet tried to do this on the scale that is required. Yes, there are a lot of so-called math ed videogames out there. Lots of them are very superficial, some are more thoughtfully designed. But they all focus primarily on skills. They use the compelling nature of videogames as a wrapper for conventional curriculum, to try to get kids to learn and practice the basic skills. But as I’ve noted, mastery of skills does not lead to mathematical thinking.

For over two thousand years, mastery of mathematical skills had to come before developing the higher level thinking because we did not have simulators. All we had was books. Now we know how to build simulators.

Based on the work I and my colleagues have done over the last four years, we have a pretty good sense of what it would take to build such a simulator. That’s where I get my figure of $100 million over five years. Building the simulator in the first place would cost around $50 million. (That was the cost of building World of Warcraft.) The remaining amount is what it would cost to build the infrastructure to support and maintain the system for use across the nation. Once in place, it could be self-sustaining through user subscriptions.

Cheers,
Maria Droujkova
http://www.naturalmath.com

Make math your own, to make your own math.

--
You received this message because you are subscribed to the Google Groups "MathFuture" group.
To post to this group, send email to mathf...@googlegroups.com.
To unsubscribe from this group, send email to mathfuture+...@googlegroups.com.
For more options, visit this group at http://groups.google.com/group/mathfuture?hl=en.

[Sue VanHattum]

Maria,

Has he posted the statement below somewhere public? I think it's a mistake to not address what happens to kids when they're younger.

I'll try to think of some questions...

Warmly,
Sue

---

From: drou...@gmail.com
Date: Fri, 21 May 2010 07:04:15 -0400
Subject: [Math 2.0] QUESTIONS PLEASE: Inviting Keith Devin to speak about his project
To: mathf...@googlegroups.com

---

Hotmail is redefining busy with tools for the New Busy. Get more from your inbox. See how.

[Anna-Marie Robertson]

This could have been done in a Google Wave.

But here is my question>

Have you considered doing this project in a virtual world? Would this project be able to run in a Virtual World?

Anna-Marie Robertson

[Maria Droujkova]

On Fri, May 21, 2010 at 9:16 AM, Sue VanHattum <suevan...@hotmail.com> wrote:

Maria,

Has he posted the statement below somewhere public? I think it's a mistake to not address what happens to kids when they're younger.

I'll try to think of some questions...

Warmly,
Sue

Sue,

The statement was posted back in February on EdBlog. There are three comments there: http://thirteencelebration.org/blog/edblog/edblog-wanted-an-apollo-program-for-math/1660/

More recently (this Thursday), Jerry Becker posted it on his MathEdNews: http://mathforum.org/kb/forum.jspa?forumID=323 There are no comments yet, but people usually send comments directly to Jerry because of the forum atmosphere, and because he distributes this as an email newsletter. He compiles the comments sometimes, but rarely in a day or two after a posting.

Ihor also found this video where Keith gives an interview: http://www.youtube.com/watch?v=z9s5T5igyYM It has 242 views an no comments.

Please do formulate some questions, about younger kids or other topics. There got to be a broader and louder conversation about this.

Off: I think you will also enjoy talking with Peter Gray on the 9th. Your blog is in his article that's making rounds now.

Cheers,
Maria Droujkova
http://www.naturalmath.com

Make math your own, to make your own math.

[Colleen King]

Here are some of my questions. It may sound like I oppose this plan but I'm really just playing devil's advocate. I am extremely interested in this idea. It reminds me of some of the work that has been done in virtual worlds. I think many of us had hoped Second Life and, later, Reaction Grid could work as a math simulator.

 

 

1. What would a math simulator look like? Is there a unifying story or plot or will there be a system of unrelated challenges? 

 

 

 

2.

The method is simulation. That’s the way we train pilots to fly aircraft, the way we train astronauts to fly the shuttle and to work in the Space Station, the way we train surgeons, and the way the US Army trains soldiers before they go anywhere near the battlefield. And that’s the way we should train young people to think mathematically.

 

In these examples, simulation is being used by a small group of highly capable people; people with the necessary prerequisite skillset. A math simulator would have to accommodate a wide spectrum of learning styles and preferences. How would the simulator prepare a diverse group of learners?

 

 

3.

Mathematics is a way of thinking about problems and issues in the world. Get the thinking right and the skills come largely for free.

 

I like the idea of a simulator in theory and I do agree that the goal is mathematical thinking. However, in my experience with students, skills really haven't come for free no matter how well problem solving and other applications have been presented. How will this project balance mathematical thinking with skill building?

 

 

4. How will students' progress be assessed? How will we know this is working? Will state tests and standards need to be modified if the simulator replaces current math curricula?

 

 

5. Would the simulator follow the current scope and sequence of math topics or will that also be revised?

 

 

6. I would think there would be significant opposition from textbook publishers and other groups. How will this be handled?

[Sue VanHattum]

Those are great questions, Colleen! Reading your questions makes me more interested in attending this.

Warmly,
Sue

---

Hotmail has tools for the New Busy. Search, chat and e-mail from your inbox. Learn more.

[Ihor Charischak]

Hi,

Keith could be our way to give Math 2.0 more visibility. Here's the press release on 2/18/10 http://news.stanford.edu/pr/2010/pr-devlin-aaas-mathematics-021910.html

 I'm wondering if he has made any progress toward's this vision. Maybe we can give him a push.

Here's details about his center H-STAR at Stanford.

http://hstar.stanford.edu/cgi-bin/?about_us

Worth exploring....

-Ihor

[Alexander Bogomolny]

Keith builds his argument on the fact that pilots and surgeons are being trained on simulators. All of them pass a highly competitive and exausting set of tests before being let in a simulator. In the very least, Keith's simulator has to have an adaptation facility to accommodate every child.

 

And, of course, there is a question of whether they'll emerge out of there with the sufficient proficiency as required for further educational choices. Will their distinct inclinations and plans for the future will be accounted for?

 

What age groups are envisaged to be using the facility? Assuming this is done up to the middle school, is there any assurance that the kids will flock to the high school math classes and meet success?

 

What would be a teacher role?

 

Alex

[Maria Droujkova]

Two references I'd like to add, since World of Warcraft was mentioned there:
http://wowinschool.pbworks.com/
http://cognitivedissonance.guildportal.com/Guild.aspx?GuildID=228854&TabID=1927706

And a question: Why do we need one centralized Platform? As opposed to using web as a platform, with all the wealth of stuff there, including giants like Warcraft and Eve, and all the way to little Scratch applets a kid can write in an afternoon...

Cheers,
Maria Droujkova
http://www.naturalmath.com

Make math your own, to make your own math.

On Fri, May 21, 2010 at 7:04 AM, Maria Droujkova <drou...@gmail.com> wrote:

Hello,

Several Math 2.0 members want to invite Keith to our weekly series and talk to him live about a math program his think tank envisions. I think we could have a valuable conversation, especially about OERs, grassroots movements, and blended financing. I would like everybody who reads this to ask a question they would ask Keith, as an experimental pre-meeting activity. One value this network has is in constructive, on-topic, deep questions we ask.

So, QUESTIONS PLEASE.

[Ihor Charischak]

On May 21, 2010, at 12:30 PM, Colleen King wrote:

> Here are some of my questions. It may sound like I oppose this plan but I'm really just playing devil's advocate

These are good, tough to answer questions. I wonder if he has as yet thought more deeply about the details. Some of the opposition forces are already starting to gather in the wings pilling up their ammo...

-Ihor

[Ihor Charischak]

On May 21, 2010, at 3:12 PM, Maria Droujkova wrote:

> And a question: Why do we need one centralized Platform? As opposed to using web as a platform, with all the wealth of stuff there, including giants like Warcraft and Eve, and all the way to little Scratch applets a kid can write in an afternoon...

I don't think he's looking for one centralized platform, but rather a place where folks want to go to learn stuff in an interesting way and doing math is a big part of it - like Google is to search... but then they are trying to become one centralized platform... a little like what Apple is turning into. The math 2.0 simulator does not have to rule the world, just become an important object in it.

-Ihor

[Maria Droujkova]

On Fri, May 21, 2010 at 4:00 PM, Ihor Charischak <iho...@me.com> wrote:

On May 21, 2010, at 3:12 PM, Maria Droujkova wrote:

> And a question: Why do we need one centralized Platform? As opposed to using web as a platform, with all the wealth of stuff there, including giants like Warcraft and Eve, and all the way to little Scratch applets a kid can write in an afternoon...

I don't think he's looking for one centralized platform, but rather a place where folks want to go to learn stuff in an interesting way and doing math is a big part of it -  like Google is to search... but then they are trying to become one centralized platform... a little like what Apple is turning into.  The math 2.0 simulator does not have to rule the world, just become an important object in it.

-Ihor

Ahhh, an adaptive learning math engine to run on the web?

There's a lot of development going on, too: Knewton, netTrekker.

Except this one's a simulator too? Something like Alternate Reality Game, but not necessarily with "real world as a platform." http://en.wikipedia.org/wiki/Alternate_reality_gam

Cheers,
Maria Droujkova
http://www.naturalmath.com

Make math your own, to make your own math.

[Ihor Charischak]

My "question" is one that I would like to ask Keith before the interview:

Give us an update on any activities that your center has done in moving toward this simulator vision.

Without knowing that answer its hard for me to come up with questions that are appropriate to ask.

He may not have done any serious thinking beyond what he has written. He may be more interested to learn from us about making something like this happen since we have more experience with the communities that would sign on to his project.

-Ihor

On May 21, 2010, at 3:12 PM, Maria Droujkova wrote:

[Colleen King]

Some of the opposition forces are already starting to gather in the wings pilling up their ammo...

 

Ihor,

 

I hope you don't think I am in opposition (need a winky/smiley face after a statement like that :)) I just think that anyone who wants the public or government to fund a $100 million project should anticipate a few challenging questions. The questions I asked were things that I had thought about in relation to my own projects. I spent over a year developing math simulations in Second Life for middle school students back in 2007. A lot of educators were really excited about the possibilities but three years have passed and nothing much came of it. I know Marc Prensky was developing an algebra game whose tagline was "play the game, pass the course". That was at least 5 years ago and the project has stalled indefinitely. There are a lot of great ideas that just never come to fruition.

 

I fully support the idea of a math simulator. In fact, I would even love to work on the project in some capacity. I want Keith Devlin to be a guest so we can all explore this idea more fully. I hope he is open to such a conversation. I'm not optimistic that he will be but I'm anxious to be proved wrong.

 

Cheers,

 

Colleen

[Maria Droujkova]

Rob Tucker on O'Reilly Radar makes an important point about ownership, and there's a lively discussion:

http://radar.oreilly.com/2010/04/ed-20-the-importance-of-owners.html

Bryce, in comments, calls Keith's idea "World of Mathcraft" and is concerned about aiming for extrinsic tools like progress tracking and achievements (the bane of World of Warcraft of late, alas).

Curiously, there are very few mentions of H-STAR in the blogs, overall.

[Ihor Charischak]

Colleen,

On May 21, 2010, at 7:57 PM, Colleen King wrote:

I hope you don't think I am in opposition (need a winky/smiley face after a statement like that :)) I just think that anyone who wants the public or government to fund a $100 million project should anticipate a few challenging questions. The questions I asked were things that I had thought about in relation to my own projects. I spent over a year developing math simulations in Second Life for middle school students back in 2007. A lot of educators were really excited about the possibilities but three years have passed and nothing much came of it. I know Marc Prensky was developing an algebra game whose tagline was "play the game, pass the course". That was at least 5 years ago and the project has stalled indefinitely. There are a lot of great ideas that just never come to fruition.

No, not at all. I agree with needing to ask tough questions. I just hope he is up to tackling them.

 I fully support the idea of a math simulator. In fact, I would even love to work on the project in some capacity. I want Keith Devlin to be a guest so we can all explore this idea more fully. I hope he is open to such a conversation. I'm not optimistic that he will be but I'm anxious to be proved wrong.

Yes, I'm a bit skeptical myself. He is a good guy and gave an excellent speech at the 2004 NCTM annual 

http://www.nctm.org/conferences/content.aspx?id=1270

Certainly worth the effort to get him.

What I think is needed is a team effort something along the lines of what  Sue VanHattum is doing in writing her book. Start with a framework for what is needed and then get key people to contribute to it and come away with a prototype. Since software doesn't come cheap, we need a person like keith who has or could raise the resources need to make it happen. I'm starting to dream again...

-Ihor

[Ihor Charischak]

On May 21, 2010, at 8:29 PM, Maria Droujkova wrote:

Rob Tucker on O'Reilly Radar makes an important point about ownership, and there's a lively discussion:

http://radar.oreilly.com/2010/04/ed-20-the-importance-of-owners.html

Bryce, in comments, calls Keith's idea "World of Mathcraft" and is concerned about aiming for extrinsic tools like progress tracking and achievements (the bane of World of Warcraft of late, alas).

Here's Bryce's actual quote:

The other route to making rewards immediate is to make them mostly artificial. I read about Keith Devlin (H-STAR, Stanford), who wants to create a World of Mathcraft game (an MMORPG that teaches mathematics principles in a natural, immersive way). I don't know if such an approach would be effective, but I do worry that it's abandoning the ideal that students should be interested in the material for its own sake, rather than for external motivators.

If its strictly external motivation then its not worth going there. There's plenty of that out there already. Intrinsic motivation is the key and I think Seymour Papert, Alan Kay etc. have helped us see how that is possible.

-Ihor

[Costello, Rob R]

(i) has he looked at using existing game engines?
(possibly much more economical - see below)

(ii) are there any articles or demos / proof of concepts that can be shared

(iii) i wonder how well can math be mapped into game / simulations?


here, for example, is a project i was involved in, which took the first person shooter, Unreal Tournament, and turned it into a simulation for learning sustainability)

http://www.thinkingcurriculum.com/thoughts/index.php/2008/11/03/virtual-house/

cost : < 20,000

we often talked at that uni about doing something else for maths learning - eg a CSI scene where you reconstruct a bullet trajectory - seeing the maths etc

as a school teacher, i experimented a little these ideas

(eg here : http://thinkingcurriculum.decenturl.com/linerider
and here :
http://thinkingcurriculum.decenturl.com/flipside-2


cheers

rob

-----Original Message-----
From: mathf...@googlegroups.com on behalf of Maria Droujkova
Sent: Fri 5/21/2010 9:04 PM
To: mathf...@googlegroups.com
Subject: [Math 2.0] QUESTIONS PLEASE: Inviting Keith Devin to speak about his project

Hello,

Several Math 2.0 members want to invite Keith to our weekly series and talk
to him live about a math program his think tank envisions. I think we could
have a valuable conversation, especially about OERs, grassroots movements,
and blended financing. I would like everybody who reads this to ask a
question they would ask Keith, as an experimental pre-meeting activity. One
value this network has is in constructive, on-topic, deep questions we ask.

So, QUESTIONS PLEASE. I will start:

- Keith, do you want the resulting system to become an OER (open education
resource) available worldwide? Why or why not?

~*~*~*~*~*
WANTED: An Apollo Program for Math

- No Related Post

Important - This email and any attachments may be confidential. If received in error, please contact us and delete all copies. Before opening or using attachments check them for viruses and defects. Regardless of any loss, damage or consequence, whether caused by the negligence of the sender or not, resulting directly or indirectly from the use of any attached files our liability is limited to resupplying any affected attachments. Any representations or opinions expressed are those of the individual sender, and not necessarily those of the Department of Education and Early Childhood Development.

[toma...@gmail.com]

Not to derail the conversation, but perhaps diverge momentarily, I
would like to offer the following from George Siemen's Twitter feed:
http://bit.ly/avvP7A /via @gsiemens

This Twitter comment led to a blog post to an article to a
reflection,....

I think there is research to support our investing public funds in
software development if the resulting application is opensource and
serves to advance our understanding of the world we live in.
I have grave reservations about licensed, restricted or copyright
code in the same way I find licensing knowledge morally problematic.

Collaborate on the development of an application because it helps you
to make sense of the world. Share it openly. Learn and teach from and
with your students. Place value in the process not the product and
leave with more questions than you came with.

Humbly submitted,
Tom

[Maria Droujkova]

Tom,

Adding your comments to the list. Yesterday's "XKCD" comic: http://xkcd.com/743/

I taught a little homeschool "unclass" on visual literacy this Spring. My favorite site for it, with the great "periodic table of tools," is here: http://www.visual-literacy.org/periodic_table/periodic_table.html

They have other tools and articles. I think some of the methods in the article you linked aren't in this "periodic table" though. I just added  Flare, the open-source software used to make several illustrations in the article, to the Prezi I am (slowly) building about types of Math 2.0: http://prezi.com/xoiiuj6rhs7p/

If anyone wants to work on this Prezi too, please let me know and I will add you.

Cheers,
Maria Droujkova
http://www.naturalmath.com

Make math your own, to make your own math.

[Jon Awbrey]

Very pretty !!!

Don't forget logical graphs --

http://mywikibiz.com/Logical_graph

Jon Awbrey

inquiry list: http://stderr.org/pipermail/inquiry/
mwb: http://www.mywikibiz.com/Directory:Jon_Awbrey
knol: http://knol.google.com/k/-/-/3fkwvf69kridz/1
oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey

[Maria Droujkova]

That's an amazing kiddie class waiting to happen, Jon! Thanks for the article. Is anyone here involved in Planet Math (a reference given there)? http://planetmath.org/ Or knows anyone who's involved?

Cheers,
Maria Droujkova
http://www.naturalmath.com

Make math your own, to make your own math.

[Costello, Rob R]

something about this troubles me ...

i can agree with the some of the sentiment, of being a colearner with students, sharing and remixing knowledge across sites,
caring about process etc etc .... once one has something cool to work with

yet also sounds like a mantra for a guild of teachers ... not for effective development of rich software environments - as much as i am passionate that these groups and functions should overlap - my job is both - i've seen nothing that says that open source approaches necessarily do it better - certainly the open source efforts on OLPC, for all of its commendable effort, is hardly a poster child for the idea

i like teaching with Scratch, Etoys, Gamemaker, Alice ...have taught kids, have learnt from them, have taught teachers etc etc ... i'm currently using and learning various other software tools and languages etc

but some focussed core - maybe with a small number of guru developers who have rich conceptual ideas - has to develop a platform in the first place (look at etoys, geogebra, scratch, gamemaker, and game modding)

doesn't really bother me if the effort or the result is commercial or open source or somewhere between - or whether or not i can get at the ultimate source code ... as long as there are enough interesting tools and ways to recombine the objects and ideas

for example, gamemaker can do rich mathematical modelling, but is not open source

nor, strictly speaking, is scratch .. even though i can see the source code in the latter case

i've also seen uni students make rich 3D games - and run classes for year 9 students - by utilising the fact that some commercial game engines provide educational licences for game modding ... which is not yet feasible from purely open source engines, as far i can see

and contra the xkcd cartoon- and educational support for the open source ideals - there is also truth is this pragmatic view: http://xkcd.com/664/

and lest facebook seem a consequence of not holding firm to open source - a dubious proposition - google, which we presumably would see as less evil, is also in court for privacy violations at present .. .not so simple that adherence to open source must deliver better outcomes - not that i mind it; but it does not guarantee anything; i think its better to tolerate a mixed economy of ideas and approaches

if Bill Gate's anti malarial efforts came to a town near you, would you resist because there is evil M$ money behind the beneficence?

On Fri, May 21, 2010 at 11:00 PM, Toma...@gmail.com <toma...@gmail.com>wrote:

> Not to derail the conversation, but perhaps diverge momentarily, I would
> like to offer the following from George Siemen's Twitter feed:
> http://bit.ly/avvP7A /via @gsiemens
>
> This Twitter comment led to a blog post to an article to a reflection,....
>
> I think there is research to support our investing public funds in software
> development if the resulting application is opensource and serves to advance
> our understanding of the world we live in.
> I have grave reservations about licensed, restricted or copyright code in
> the same way I find licensing knowledge morally problematic.
>
> Collaborate on the development of an application because it helps you to
> make sense of the world. Share it openly. Learn and teach from and with your
> students. Place value in the process not the product and leave with more
> questions than you came with.
>
> Humbly submitted,
> Tom
>

--
You received this message because you are subscribed to the Google Groups "MathFuture" group.
To post to this group, send email to mathf...@googlegroups.com.
To unsubscribe from this group, send email to mathfuture+...@googlegroups.com.
For more options, visit this group at http://groups.google.com/group/mathfuture?hl=en.

Important - This email and any attachments may be confidential. If received in error, please contact us and delete all copies. Before opening or using attachments check them for viruses and defects. Regardless of any loss, damage or consequence, whether caused by the negligence of the sender or not, resulting directly or indirectly from the use of any attached files our liability is limited to resupplying any affected attachments. Any representations or opinions expressed are those of the individual sender, and not necessarily those of the Department of Education and Early Childhood Development.

[Feldon, Fred]

Hi, Colleen -- Do you still have any math activities for students in Second Life? Are you still active in Second Life? Let us know. Thanks! -- Fred Feldon (SL: ffeldon Mint)

Fred Feldon
Department Chair, Mathematics
Coastline Community College
(714) 546-7600 x11336; Fax (714) 241-6287
ffe...@coastline.edu


________________________________

From: mathf...@googlegroups.com on behalf of Colleen King
Sent: Fri 5/21/2010 4:57 PM
To: mathf...@googlegroups.com
Subject: Re: [Math 2.0] Re: QUESTIONS PLEASE: Inviting Keith Devin to speak about his project


Ihor,

I hope you don't think I am in opposition (need a winky/smiley face after a statement like that :)) I just think that anyone who wants the public or government to fund a $100 million project should anticipate a few challenging questions. The questions I asked were things that I had thought about in relation to my own projects. I spent over a year developing math simulations in Second Life for middle school students back in 2007. A lot of educators were really excited about the possibilities but three years have passed and nothing much came of it. I know Marc Prensky was developing an algebra game whose tagline was "play the game, pass the course". That was at least 5 years ago and the project has stalled indefinitely. There are a lot of great ideas that just never come to fruition.

I fully support the idea of a math simulator. In fact, I would even love to work on the project in some capacity. I want Keith Devlin to be a guest so we can all explore this idea more fully. I hope he is open to such a conversation. I'm not optimistic that he will be but I'm anxious to be proved wrong.

Cheers,

Colleen

[Colleen King]

Hi Fred,

 

Unfortunately, I left Second Life about two years ago. I felt there wasn't enough interest in my work to justify all the time I was spending in-world. Apart from Peggy Sheehy's Ramapo Island, Global Kids, and few other educational initiatives, learning in Second Life never materialized for middle school students. I haven't really followed Second Life very closely since then. I know some graphing and data visualization tools were made. I guess Scratch has been ported to SL as well. Have there been other developments in the area of math instruction?

 

I had become interested in the idea of SL as a learning environment in 2006 and spent all of 2007 developing some ideas. I had taken the concept of Seymour Papert's logo turtle and created a three dimensional version I called the logo bee. Students could write simple programs that the bee would then execute. The result would be these amazing 3D structures. You could program towers and bridges made of various prisms and pyramids. And there would be the thrill of watching the bee bring the programs to life. I also built a logo operated robot. This tool was used more for rate, time, distance, and graphing activities. Later I started building real-life math simulations. The idea was to recreate everyday math experiences. 

 

I think people saw the potential of these ideas but without any students to actually use the tools, it became pointless. I went back to creating web-based math activities and focused on projects that had more immediate (and, therefore, more satisfying) results.

 

What sort of math projects are you doing?

 

Colleen King

[LFS]

Hiya,

Maybe this is not the place for this. Just ignore. But I have been thinking so hard about this and didn’t know where to post.

Something that always confused me in school was the connection between Function Rule, Table of Values, Graph  - primarily because we use a “generic” format and yet each problem has its own restrictions. I particularly hated the term “Table of Values”, because usually it was just “Table of SOME Values”.

==

Problem 1: My boss gives me 5 shirts to sell. I make a profit of $30 per shirt. http://geogebrawiki.pbworks.com/Modeling_ShirtProblem

Problem 2: I drive 5 hours at 30mph.  http://geogebrawiki.pbworks.com/Modeling_DriveProblem  - I love the dynamic table and it is easy to make!

==

I am thinking that GeoGebra  gives us the ability to write “complete descriptions” since we have

(a)    Algebra View so we can define rules and functions, limit them to intervals, ….

(b)   Graphics View and we can label the axis, the units, etc.

(c)    Spreadsheet View and we can make dynamic tables of values, convert automatically to lists and get idea of function.

==

Yesterday someone linked me to: http://www.dec.utexas.edu/askme/unit1.html#activity10 which is called Four-Corner Model.

 

QUESTIONS:

1. Would the answer to the Four Corner Model for these 2 problems be different?

2. Do kids get understand that tables are sometimes complete and sometimes not and that functions sometimes give bad information (like selling 1/2 a shirt) ?

3. What do you think of “Descriptions” with technology like GeoGebra?

 

I would be grateful for any insight/ experience/ feedback etc.

Linda

--------------------------------

Goal: To create GeoGebra Challenge for modeling (see e.g. http://www.youtube.com/watch?v=9th6fvaO3EM )

[Jon Awbrey]

That's an interesting triad --

The three aspects of definition that you mention
are described in classical philosophy of science
under the following headings:

Intensional Definition -- formulas, procedures, programs, rules
Extensional Definition -- graph of all ordered pairs (x, f(x))
Enumerative Definition -- finite sample of cases under concept

Jon Awbrey

LFS wrote:
> Hiya,
>
> Maybe this is not the place for this. Just ignore. But I have been thinking
> so hard about this and didn't know where to post.
>
> Something that always confused me in school was the connection between
> Function Rule, Table of Values, Graph - primarily because we use a
> "generic" format and yet each problem has its own restrictions. I
> particularly hated the term "Table of Values", because usually it was just
> "Table of SOME Values".

--

inquiry list: http://stderr.org/pipermail/inquiry/
mwb: http://www.mywikibiz.com/Directory:Jon_Awbrey
knol: http://knol.google.com/k/-/-/3fkwvf69kridz/1
oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey

[LFS]

Thank-you Jon - I love the words. Intentional, Extensional, Enumerative.
And I REALLY like that the last one specifically says "finite".
Linda

-----Original Message-----
From: mathf...@googlegroups.com [mailto:mathf...@googlegroups.com] On
Behalf Of Jon Awbrey
Sent: Tuesday, May 25, 2010 2:05 PM
To: mathf...@googlegroups.com

[Jon Awbrey]

Yes, working on the assumption of mortal learners,
the notion -- going back to Aristotle, and later
revived by C.S. Peirce -- is supposed to reflect
the fact that our personal sample of experience
in any domain is always finite, and we have to
form our concepts of the whole idea from that,
depending on how you feel about the balance
between nature and nurture, perhaps given
a leg up by our species evolution in the
form of "innate" sources of information.

Jon

[Colleen King]

Hi Linda,

 

This is most certainly the right place for your question.

I hope to see more questions like this.

Around my area, we refer to this as the Rule of Four or simply "multiple representations". Some teachers ask students to fold a piece of paper into fourths and describe the problem differently in each quadrant. I think Geogebra offers a better way for students to model math problems.

 

1. Would the answer to the Four Corner Model for these 2 problems be different?

Only the verbal description would be different. If you worked backwards and showed students the table of values containing fractional numbers, the story about selling individual shirts would not be a good verbal model.

2. Do kids get understand that tables are sometimes complete and sometimes not and that functions sometimes give bad information (like selling 1/2 a shirt) ?

Students who use the Rule of Four are more likely to make that connection than those who do not. I really like how you show this in your examples. 

3. What do you think of “Descriptions” with technology like GeoGebra?

I think this is brilliant and should be explored further. I would encourage you to apply this to other types of problems and, perhaps, give a presentation.

Colleen

[Feldon, Fred]

Hi, Colleen -- I hear you about SL not quite "taking off" as I had hoped, especially with the notation required in math. But I feel like interest is slowly growing.

Our College has a SL underwater experiment where the ocean floor is marked off and students count the number and types of fish that swim by then do a statistical analysis. Another math ed class has students "practice teach" in SL to the rest of the class. I, personally, am working on streaming my Tablet PC desktop using digital ink to write mathematically into SL onto a prim surface which the new Viewer 2 allows, but my computer is a couple years old and needs updating. Neither of my two computer's hardware will support my needs yet but it's coming! -- Fred

________________________________

To unsubscribe from this group, send email to mathfuture+...@googlegroups.com <mailto:mathfuture%2Bunsu...@googlegroups.com> .

[LFS]

Hiya Colleen,

Thank you so much for your detailed response – that was exactly what I was hoping for so that I could see if I was looking at this problem in a useful way.

I will think about this more. In 8^th grade I had this fantastic teacher who made us write with words: Let x=# shirts sold. Then x can be 0,1,…,5.  on one line and then the next line was:  Let  y=profit in $. Then y=30x. Everything had to have words and units. It was SUCH a bore – but I swear it was the single most important tool I learned.

(P.S.  I did not even think about the fact that problems are often worked backwards and forwards as with your response to Q1.)

Thanks again,

Linda

 

From: mathf...@googlegroups.com [mailto:mathf...@googlegroups.com] On Behalf Of Colleen King

Sent: Tuesday, May 25, 2010 8:37 PM
To: mathf...@googlegroups.com

[Maria Droujkova]

On Tue, May 25, 2010 at 2:36 PM, Colleen King <mathpla...@gmail.com> wrote:

Hi Linda,

 

This is most certainly the right place for your question.

I hope to see more questions like this.

Around my area, we refer to this as the Rule of Four or simply "multiple representations". Some teachers ask students to fold a piece of paper into fourths and describe the problem differently in each quadrant. I think Geogebra offers a better way for students to model math problems.

LHS,

To follow up on Colleen's ideas, there are a few good works specifically about multiple representations in computer environment. The interesting tidbit I took home from these studies is the utmost importance of DYNAMIC LINKS among multiple representations that only computer systems can provide. Nothing in the physical world comes even close to these automatic feedback loops between, say, a manipulative and its mathematical symbolization, or text and graph. A few of Montessori materials were designed for "automatic feedback" for correctness, or for linking two representations on the front and the back of a card, so the idea of such links is old. However, until computers, only a human (not any gizmo) could provide dynamic links among representations interactively.